I have thick skin growing from under my toenail, what is that?

It could be fungus. Toenail fungal infections, onychomycosis, are characterized by thicking of the nail plate, discoloration ( usually yellowish brown) lossening of the nail and accumulation of debris between the nail plate and nail bed. It is also possible that you are developing a corn on the end of your toe as a result of the toe being too long or becoming deformed. A quick exam can determine this.
A corn. It can be a corn (callus tissue) caused by pressure of the shoe on the toe and by a thickened nail. Sometimes this is actually a soft tissue lesion (such as a fibroma) or might lie over a bone spur under the nail. See a podiatrist to make the diagnosis, and get treatment options.